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Knowledge graph embedding models have gained significant attention in AI research. The aim of knowledge graph embedding is to embed the graphs into a vector space in which the structure of the graph is preserved. Recent works have shown that the inclusion of background knowledge, such as logical rules, can improve the performance of embeddings in downstream machine learning tasks. However, so far, most existing models do not allow the inclusion of rules. We address the challenge of including rules and present a new neural based embedding model (LogicENN). We prove that LogicENN can learn every ground truth of encoded rules in a knowledge graph. To the best of our knowledge, this has not been proved so far for the neural based family of embedding models. Moreover, we derive formulae for the inclusion of various rules, including (anti-)symmetric, inverse, irreflexive and transitive, implication, composition, equivalence, and negation. Our formulation allows avoiding grounding for implication and equivalence relations. Our experiments show that LogicENN outperforms the existing models in link prediction.

In recognition memory, anything that is objectively new is necessarily not-old, and anything that is objectively old is necessarily not-new. Therefore, judging whether a test item is new is logically equivalent to judging whether it is old, and conversely. Nevertheless, a series of 10 experiments showed that old? and new? judgments did not produce equivalent recognition accuracy. In Experiments 1-4, wherein subjects made old? or new? judgments about test items, new? judgments yielded more accurate performance for old items than old? judgments did, and old? judgments yielded more accurate performance for new items than new? judgments did. This same violation of logical equivalence was observed in Experiments 5-10, wherein subjects made similar? judgments as well as old? and new? ones. In short, old? and new? judgments displayed consistent Judgment × Item crossovers, rather than equivalence. Response latencies were used to test the hypothesis that Judgment × Item crossovers were due to certain judgment-item combinations provoking more deliberate, thorough retrieval than other combinations. There was no support for that hypothesis, but the data were consistent with an earlier theory, which posits that latency depends on the extent to which judgments or items slant retrieval toward accessing verbatim traces. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

We introduce the problem of clustering the set of vertices in a given 3D mesh. The problem is motivated by the need for value engineering in architectural projects. We first derive a max-norm based metric to estimate the geometric disparity between a given pair of vertices, and characterize the problem in terms of this measure. We show that this distance can be computed by using Sequential Quadratic Programming (SQP). Next we introduce two different algorithms for clustering the set of vertices on a given mesh, respectively based on two disparity measurements: max-norm and L2-norm based metric. An equivalence is established between mesh vertices and physical joints in an architectural mesh. By replacing individual joints by their equivalent cluster representative, the number of unique joints in the facade mesh, and therefore the fabrication cost, is dramatically reduced. Finally, we present an algorithm for remeshing a given surface in order to further reduce the number of joint clusters. The framework is tested for a set of real-world architectural surfaces to illustrate the effectiveness and utility of our approach. Overall, this approach tackles the important problem reducing fabrication cost of joints without modifying the underlying connectivity that was specified by the architect.

The existing small-signal analysis models do not adequately describe the impact of the types of disturbance on the torque-frequency dynamics of the multi-VSC parallel system. In this paper, based on the principle of electromechanical analogy, a unified equivalent admittance modeling method is proposed by analogizing the rotor dynamic model of a synchronous generator (SG) to the circuit network, which has the advantages of simple modeling, clear physical meaning and easy expansion. Firstly, the equivalent admittance model of a single SG/VSC is established, and then easily extended to the multi-VSC system. The proposed modelling method not only applicable to a variety of VSCs, but also can handle different types of disturbance. More importantly, the circuit theory can be applied to analyze the torque-frequency dynamic characteristics. Subsequently, the equivalence between the proposed model and the state-space model under different damping terms is compared. In addition, the response characteristics of two different damping terms are compared. Next, the dynamic response characteristics of single VSC and multi-VSC parallel systems under different disturbances are analyzed. Finally, related simulations and experiments are executed to verify the accuracy and effectiveness of the proposed method.

Mathematical tools are fundamental for control methods, but it is unclear how control impacts mathematics. This paper attempts to give an answer with focus on solving linear algebraic equations (LAEs) from the perspective of systems and control. By proposing an iterative method that integrates a learning control mechanism, a class of tracking problems for iterative learning control (ILC) is explored for the problem solving of LAEs. A trackability property of ILC is newly developed, by which analysis and synthesis results are established to disclose the equivalence between the solvability of LAEs and the controllability of discrete control systems. Hence, LAEs can be solved by equivalently achieving the perfect tracking tasks of resulting ILC systems via the classic state feedback-based design and analysis methods. It is shown that the solutions for any solvable LAE can all be calculated with different selections of the initial input. Moreover, the presented ILC method is applicable to determining all the least squares solutions of any unsolvable LAE. In particular, a deadbeat design is incorporated to ILC such that the solving of LAEs can be completed within finite iteration steps.

The study of consistency in decision-making models is of great importance. Our proposal deals with a special type of extended aggregation functions to guarantee consistency that is based on T-S consistency of linearly ordered fuzzy preference relations (fuzzy ranking for preferences). Necessary conditions to ensure consistency in the aggregation process are provided. Moreover, sufficient conditions to guarantee the existence of extended aggregation functions verifying T-S consistency are presented. Some examples of functions of this type are also given. The equivalence between T-S consistency and the additive consistency for fuzzy preference relations is established.

Tensor singular value decomposition (t-SVD) has recently become increasingly popular for tensor recovery under partial and/or corrupted observations. However, the existing t -SVD-based methods neither make use of a rank prior nor provide an accurate rank estimation (RE), which would limit their recovery performance. From the practical perspective, the tensor RE problem is nontrivial and difficult to solve. In this article, we, therefore, aim to determine the correct rank of an intrinsic low-rank tensor from corrupted observations based on t-SVD and further improve recovery results with the estimated rank. Specifically, we first induce the equivalence of the tensor nuclear norm (TNN) of a tensor and its f -diagonal tensor. We then simultaneously minimize the reconstruction error and TNN of the f -diagonal tensor, leading to RE. Subsequently, we relax our model by removing the TNN regularizer to improve the recovery performance. Furthermore, we consider more general cases in the presence of missing data and/or gross corruptions by proposing robust tensor principal component analysis and robust tensor completion with RE. The robust methods can achieve successful recovery by refining the models with correct estimated ranks. Experimental results show that the proposed methods outperform the state-of-the-art methods with significant improvements.

How many scenarios are sufficient to validate the safe Operational Design Domain (ODD) of an Automated Driving System (ADS) equipped vehicle Is a more significant number of sampled scenarios guaranteeing a more accurate safety assessment of the ADS Despite the various empirical success of ADS safety evaluation with scenario sampling in practice, some of the fundamental properties are largely unknown. This paper seeks to remedy this gap by formulating and tackling the scenario sampling safety assurance problem from a set invariance perspective. First, a novel conceptual equivalence is drawn between the scenario sampling safety assurance problem and the data-driven robustly controlled forward invariant set validation and quantification problem. This paper then provides a series of complete solutions with finite-sampling analyses for the safety validation problem that authenticates a given ODD. On the other hand, the quantification problem escalates the validation challenge and starts looking for a safe sub-domain of a particular property. This inspires various algorithms that are provably probabilistic incomplete, probabilistic complete but sub-optimal, and asymptotically optimal. Finally, the proposed asymptotically optimal scenario sampling safety quantification algorithm is also empirically demonstrated through simulation experiments.

International audience; We introduce a model of graph-constrained dynamic choice with reinforcement modeled by positively $\alpha$-homogeneous rewards. We show that its empirical process, which can be written as a stochastic approximation recursion with Markov noise, has the same probability law as a certain vertex reinforced random walk. We use this equivalence to show that for $\alpha > 0$, the asymptotic outcome concentrates around the optimum in a certain limiting sense when 'annealed' by letting $\alpha \to \infty$ slowly.

Zero-sequence circulating current (ZSCC) suppression and fault-tolerant control (FTC) are important guarantees for the safe and reliable operation of parallel T-type three-level rectifiers (PT23LRs). However, none of the existing literature can solve the FTC under the ZSCC suppression of the PT23LRs when the open switch fault (OSF) occurs in neutral-point (NP) switches. In order to solve these issues, a novel FTC method based on ZSCC suppression is proposed in this paper. Firstly, an improved finite-time controller is constructed to suppress the ZSCC by adjusting the difference of zero-sequence duty ratio between two rectifiers, completely. Then, based on the principle of area equivalence, the switching sequence is reconstructed by changing the state switching mode of fault phase in real time. As a result, the FTC under the OSF of NP switches is realized without affecting the suppression of ZSCC. Compared with the existing methods, the proposed method not only realizes the suppression of the ZSCC of the PT23LRs, but also completes the FTC under the OSF of NP switches, which guarantees the ZSCC suppression ability under the OSF of NP switches. Consequently, the power quality of AC side of the PT23LRs is improved significantly during the normal operation and the operation under the OSF of NP switches. Thus, the safe and reliable operation of the PT23LRs are guaranteed effectively. Finally, the feasibility and correctness of the proposed method is verified by experiment results.

This study aims to develop the notion of general fuzzy automata (GFA) to a new one which is known as “ L B -valued general fuzzy automata”. Instead of the term L B -valued general fuzzy automata, for simplicity, L B -valued GFA is used where B is regarded as a set of propositions about the GFA, in which its underlying structure has been a complete infinitely distributive lattice. Further, L B -valued GFA is scrutinized via different operators and also the interrelationship among these operators is examined. Specifically, it is shown that L B -valued successor, L B -valued predecessor and L B -valued residuated operators play an important role in the algebraic study of L B -valued general fuzzy automaton and that under certain conditions these operators are interrelated. In addition, the concept of a homomorphism between L B -valued general fuzzy automata is introduced and studied. Finally, the concepts of equivalence and congruence are defined, the quotient L B -valued GFA with respect to congruence is formulated and the equivalence between L B -valued GFA and its quotient automaton is proved. To clarify the notions and the results obtained in this study, some examples are submitted as well.

A fuzzy first order and second moment method (FFOSM) is proposed to efficiently estimate time-independent and time-dependent failure credibility in the presence of fuzzy uncertainty. For the time-independent linear performance function with independently, regularly and identically distributed fuzzy inputs, the analytical relationship is firstly derived between the failure credibility and fuzzy safety index, and the relation form is established between fuzzy safety index and fuzzy first two moments of the performance function. Secondly, in the standard space of fuzzy inputs, the minimum infinite norm distance from the coordinate origin to the linear limit state surface is analytically derived, and the point with the smallest infinite norm distance located on the limit state surface is defined as the fuzzy design point. Based on this definition, the geometric and physical meanings are explained for the fuzzy safety index and fuzzy design point, and the fuzzy first order and second moment method for time-independent failure credibility analysis is established for both linear and nonlinear performance function. Thirdly, for time-dependent performance functions, the equivalence is proved between time-dependent fuzzy safety index and the minimum value of transient fuzzy safety indices, on which the iteration steps of fuzzy first order and second moment method is designed for time-dependent fuzzy safety index and failure credibility estimation. Since the proposed fuzzy first order and second moment method is an approximately analytical approach, it has higher efficiency than the fuzzy simulation method and the cut level optimization method. Finally, the effectiveness and applicability of the proposed method are demonstrated by different examples.

Since the mid-1960s, it has been known that regular or deterministic flow lines (DFLs) with an arbitrary arrival process possess three essential behaviors: 1) a customer exit time recursion; 2) a server reordering principle; and 3) a delay equivalence with prototype queueing systems. Even though these three fundamental behaviors were discovered decades ago, analogous results for hybrid DFLs (HDFLs)--possessing multiple servers for each stage--have not been unearthed. In this article, we prove the existence of a recursion for customer exit times in HDFLs. This result leads naturally to a server reordering principle. Furthermore, we identify specific conditions under which the total delay faced by a customer in an HDFL is equivalent to that in a G/D/c queue. Exploiting these results, we numerically determine the proportion of HDFL systems with a delay equivalent, study the computational burdens required for HDFL simulation, and assess the performance of approximations for HDFL systems. We hope these newly identified behaviors will lead to improved approximation methods and optimization models for use in modern automated manufacturing systems.

This paper presents a new optimization-based approach to determine the class of stabilizing control structures with the necessary set of feedback links for interconnected systems. The proposed approach relies on a graph theoretic interpretation and its equivalence in terms of binary linear programs (BLP). To carry out the primary goal, first, the stabilizability of an LTI system under the decentralized control structure is presented in terms of a BLP. Next, two graph-based criteria are proposed to characterize stabilizing control structures with the required feedback links. Finally, all possible stabilizing control structures with the necessary feedback links are derived via solving a set of BLPs. In addition to the analysis of stabilizing control structures, the proposed graph-theoretic approach offers a versatile set of tools to find the simplest control structures capable of assigning the closed-loop spectrum in a totally arbitrary desired region. Simulation results illustrate the assessment of stabilizing control structures, the required additional feedback links, and the elegant generalization of the proposed approach to regional pole-placement.

Differential-algebraic equations (DAEs) are a widespread dynamical model that describes continuously evolving quantities defined with differential equations, subject to constraints expressed through algebraic relationships. As such, DAEs arise in many fields ranging from physics, chemistry, and engineering. In this article, we focus on linear DAEs, and develop a theory for their minimization up to an equivalence relation. We present differential equivalence, which relates DAE variables that have equal solutions at all time points (thus requiring them to start with equal initial conditions) and extends the line of research on bisimulations developed for Markov chains and ordinary differential equations. We apply our results to the electrical engineering domain, showing that differential equivalence can explain invariances in certain networks as well as analyze DAEs, which could not be originally treated due to their size.

In this article, a general approach for directed graph clustering and two new density-based clustering objectives are presented. First, using an equivalence between the clustering objective functions and a trace maximization expression, the directed graph clustering objectives are converted into the corresponding weighted kernel k-means problems. Then, a nonspectral algorithm, which covers both the direction and weight information of the directed graphs, is thus proposed. Next, with Rayleigh's quotient, the upper and lower bounds of clustering objectives are obtained. After that, we introduce a new definition of weak links to characterize the effectiveness of clustering. Finally, illustrative examples are given to demonstrate effectiveness of the results. This article provides a glance at the potential connection between density-based and pattern-based clustering. Compared with other approaches for directed graph clustering, the method proposed in this article naturally avoids the loss of the nonsymmetric edge data because there is no need for any additional symmetrization.

Asymmetrical six-phase induction machines are widely used in high-power safety-critical applications. The so-called pseudo six-phase winding layout has recently been proposed as a promising contender for high power medium voltage applications in terms of torque density, phase current quality, simple single-layer-based stator winding design, and fault-tolerant capability. This winding layout employs quadruple three-phase stator winding sets connected to provide only six terminals, while being fed from two three-phase inverters. Therefore, the same conventional six-phase-based control structure can still be employed. Among the different control techniques, model predictive current control is considered as one of the cutting-edge technologies for multiphase drive systems, thanks to its simplicity and flexibility in defining new control objectives. This paper investigates how the available 64 voltage vectors of a six-phase inverter are classified among different subspaces when employing a pseudo six-phase stator winding. Moreover, the required modifications to classical predictive current control (PCC) are introduced in order to properly control the machine in a manner similar to conventional asymmetrical six-phase machines while ensuring minimum circulating xy current components. The concept of virtual voltage vectors (VVVs) has also been employed to further enhance the stator current quality. The proposed controller is validated using a 2Hp prototype pseudo six-phase machine under different operating conditions. An experimental comparative study with an asymmetrical six-phase machines is also carried out to verify the claimed equivalence.

To provide timely lifetime information of manufactured products to potential customers, designing an efficient accelerated degradation test (ADT) is an important task for reliability analysts. In the literature, several papers have addressed a general k -level ADT design problem (including the determinations of the number of stress levels ( k ), testing stresses, allocation of test units and termination times) when the underlying degradation path follows an exponential dispersion model. The results are practical and interesting. However, most of those studies only addressed the case of k ≤ 4 . Generally, if a direct proof (such as using the Karush–Kuhn–Tucker conditions) for the case of k > 4 is intractable, we can consider an indirect proof via the general equivalence theorem. In this paper, we first propose a conjecture optimal design for a k -level ADT design problem and then apply the general equivalence theorem to show that this conjecture design turns out to be the global V-optimal design. In addition, an example is used to illustrate the proposed procedure. The main contribution of this work is that this analytical approach can provide reliability analysts with better insight for designing an efficient ADT plan.

A continuous-time distributed algorithm based on multi-agent systems is proposed to solve the convex nonsmooth optimization with globally coupled constraints in this paper. Firstly, the relationship of equivalence between the equilibrium and the optimal solution of the system is proved by using the properties of projection operator and saddle point. In addition, the stability of the algorithm is analyzed by means of Lie derivative and set-valued LaSalle’s invariance principle. In particular, the trajectory of the proposed algorithm from any initial point can converge to the global optimal solution. Finally, the effectiveness of the designed algorithm is verified by numerical simulations.

Researchers in the social and biomedical sciences regularly measure networks spanning entire villages in low- and middle-income countries by documenting the social contacts of just one or two representatives from participating households. This “lean” approach to network measurement is cost-effective compared to a sociometric census of a village’s adult population. However, it implicitly assumes that interviewed and non-interviewed coresidents are structurally equivalent — i.e., directly connected to the same network members in the same fashion. Drawing from research on multilevel networks and intra-household heterogeneity, here I argue that this assumption is unlikely to hold for the personal social ties typically of interest to field researchers (i.e., friends and other preferred sources and targets of material, informational and emotional support). I substantiate my claim with an exploratory case study on the similarity of coresidents’ incoming and outgoing ties using data documenting unrestricted roster-based reports on the provision of tangible aid amongst all adult residents of a remote village of indigenous horticulturalists in Nicaragua (108 adults; 32 nuclear-family households). Results indicate that coresidents markedly deviate from structural equivalence and its generalisation in the form of stochastic equivalence (i.e., similar probabilities of being directly connected to the same network members in the same fashion). All in all, it is ill-advised to assume that the personal network of any one coresident, or, more generally, the manner in which a coresident tends to send and receive their personal ties, is representative of their household.

Fuzzification of real-valued functions using the extension principle is frequently used to study engineering and economic problems when fuzzy data are taken into account. In this article, we generate a fuzzy function by fuzzifying a vector-valued function using the extension principle. On the other hand, it is also well known that the membership function of each fuzzy set can be expressed in terms of its α-level sets. Roughly speaking, each fuzzy set can be decomposed into its α-level sets. Therefore, we generate another fuzzy function by fuzzifying a vector-valued function on the basis of the decomposition form. The main focus is to establish their equivalence under some suitable conditions. Without extra conditions, we have difficulty to establish their equivalence. However, their relationship can be realized on the basis of the degree of fuzzy uncertainty. In these settings, we suggest the use of the decomposition form rather than the extension principle to fuzzify vector-valued functions.

Cloud computing enables users to remove the necessity of the need of local hardware architecture, which removes the burden of the users from high computation costs. Therefore, it has attracted much attention and research has been conducted heavily on it. To protect users' privacy, data is usually encrypted prior to being sent to the cloud server. New cryptographic primitive such as public-key encryption with equality test (PKEET) has been introduced to make it more practical. In PKEET, users can test whether the underlying messages of two ciphertexts encrypted under different public keys are equal or not without the need to decrypt those ciphertexts. This is a very useful tool, especially for the cloud database, since PKEET mainly focuses on the equality test between two ciphertexts. However, in practice, the cloud server may need to verify the equivalence among more than two ciphertexts. This leads to disclosing unnecessary information of users and redundant computation cost will also occur when using traditional PKEET schemes. How to make this more efficient and practical remains an interesting research problem. In this paper, to solve the aforementioned problems by providing a novel concept of public-key encryption with multi-ciphertext equality test (PKE-MET).

Labeling of the connected components is the key operation of the target recognition and segmentation in remote sensing images. The conventional connected-component labeling (CCL) algorithms for ordinary optical images are considered time-consuming in processing the remote sensing images because of the larger size. A dynamic run-length based CCL algorithm (DyRLC) is proposed in this paper for the large size, big granularity sparse remote sensing image, such as space debris images and ship images. In addition, the equivalence matrix method is proposed to help design the pre-processing method to accelerate the equivalence labels resolving. The result shows our algorithm outperforms 22.86% on execution time than the other algorithms in space debris image dataset. The proposed algorithm also can be implemented on the field programming logical array (FPGA) to enable the realization of the real-time processing on-board.

This study evaluated the accuracy of synthetic computed tomography (sCT), as compared to CT, for the 3D assessment of the hip morphology. Thirty male patients with asymptomatic hips, referred for magnetic resonance (MR) imaging and CT, were included in this retrospective study. sCT images were generated from three-dimensional radiofrequency-spoiled T1-weighted multi-echo gradient-echo MR images using a commercially available deep learning-enabled software and were compared with CT images through mean error and surface distance computation and by means of eight clinical morphometric parameters relevant for hip care. Parameters included center-edge angle (CEA), sharp angle, acetabular index, extrusion index, femoral head center-to-midline distance, acetabular version (AV), and anterior and posterior acetabular sector angles. They were measured by two senior orthopedic surgeons and a radiologist in-training on CT and sCT images. The reliability and agreement of CT- and sCT-based measurements were assessed using intraclass correlation coefficients (ICCs) for absolute agreement, Bland-Altman plots, and two one-sided tests for equivalence. The surface distance between CT- and sCT-based bone models were on average submillimeter. CT- and sCT-based measurements showed moderate to excellent interobserver and intraobserver correlation (0.56 0.75). For CEA, the intraobserver agreement was good (ICC > 0.75) and the interobserver agreement was moderate (ICC > 0.69). Limits of agreements were similar between intraobserver CT and intermodal measurements. All measurements were found statistically equivalent, with average intermodal differences within the intraobserver limits of agreement. In conclusion, sCT and CT were equivalent for the assessment of the hip joint bone morphology.

We propose a novel pairwise distance measure between image keypoint sets, for the purpose of large-scale medical image indexing. Our measure generalizes the Jaccard index to account for soft set equivalence (SSE) between keypoint elements, via an adaptive kernel framework modeling uncertainty in keypoint appearance and geometry. A new kernel is proposed to quantify the variability of keypoint geometry in location and scale. Our distance measure may be estimated between $O(N^2)$ image pairs in $O(N~\log~N)$ operations via keypoint indexing. Experiments report the first results for the task of predicting family relationships from medical images, using 1010 T1-weighted MRI brain volumes of 434 families including monozygotic and dizygotic twins, siblings and half-siblings sharing 100%-25% of their polymorphic genes. Soft set equivalence and the keypoint geometry kernel improve upon standard hard set equivalence (HSE) and appearance kernels alone in predicting family relationships. Monozygotic twin identification is near 100%, and three subjects with uncertain genotyping are automatically paired with their self-reported families, the first reported practical application of image-based family identification. Our distance measure can also be used to predict group categories, sex is predicted with an AUC=0.97. Software is provided for efficient fine-grained curation of large, generic image datasets., 10 pages, 8 figures

BACKGROUND AND OBJECTIVES: Loneliness is prevalent among older adults and known to be detrimental to mental health. The objective of this study was to determine the psychometric properties of the Chinese 6-item De Jong Gierveld Loneliness Scale (DJGLS) in the older native and diasporic Chinese community. RESEARCH DESIGN AND METHODS: Participants were recruited from a local community in urban Tianjin, China and urban Chinese communities of older adults in the Netherlands. Scale properties, including reliability, were calculated with Cronbach's alpha and multiple-group confirmatory factor analysis to examine the two-dimensional structure of the scale and the cross-cultural equivalence between both countries. Item response analysis was employed to plot the relationships between the item response and expected total scale score. RESULTS: A total of 193 older adults from China and 135 older adults from the Netherlands were included. The Cronbach's alphas were and 0.68 (China) and 0.71 (the Netherlands). The DJGLS's two-dimensional structure was validated by the goodness of fit and the factor loadings. Cross-cultural equivalence was demonstrated with the multiple-group confirmatory analysis. In addition, sufficient discriminative power of the individual items was demonstrated by item response analysis in both countries. DISCUSSION AND IMPLICATIONS: This study is the first to provide a detailed item behavior analysis with an item response analysis of the DJGLS. In conclusion, the findings of this study suggest that the DJGLS has adequate and similar item and scalar equivalence for use in Chinese populations.;BACKGROUND AND OBJECTIVESLoneliness is prevalent among older adults and known to be detrimental to mental health. The objective of this study was to determine the psychometric properties of the Chinese 6-item De Jong Gierveld Loneliness Scale (DJGLS) in the older native and diasporic Chinese community. RESEARCH DESIGN AND METHODSParticipants were recruited from a local community in urban Tianjin, China and urban Chinese communities of older adults in the Netherlands. Scale properties, including reliability, were calculated with Cronbach's alpha and multiple-group confirmatory factor analysis to examine the two-dimensional structure of the scale and the cross-cultural equivalence between both countries. Item response analysis was employed to plot the relationships between the item response and expected total scale score. RESULTSA total of 193 older adults from China and 135 older adults from the Netherlands were included. The Cronbach's alphas were and 0.68 (China) and 0.71 (the Netherlands). The DJGLS's two-dimensional structure was validated by the goodness of fit and the factor loadings. Cross-cultural equivalence was demonstrated with the multiple-group confirmatory analysis. In addition, sufficient discriminative power of the individual items was demonstrated by item response analysis in both countries. DISCUSSION AND IMPLICATIONSThis study is the first to provide a detailed item behavior analysis with an item response analysis of the DJGLS. In conclusion, the findings of this study suggest that the DJGLS has adequate and similar item and scalar equivalence for use in Chinese populations.

In the present paper we consider design criteria which depend on several designs simultaneously. We formulate equivalence theorems based on information matrices (if criteria depend on designs via information matrices) or with respect to the designs themselves (for finite design regions). We apply the obtained optimality conditions to multiple-group random coefficient regression models and illustrate the results by simple examples.

We address Bayesian persuasion between a sender and a receiver with state-dependent quadratic cost measures for general classes of distributions. The receiver seeks to make mean-square-error estimate of a state based on a signal sent by the sender while the sender signals strategically in order to control the receiver's estimate in a certain way. Such a scheme could model, e.g., deception and privacy, problems in multi-agent systems. Existing solution concepts are not viable since here the receiver has continuous action space. We show that for finite state spaces, optimal signaling strategies can be computed through an equivalent linear optimization problem over the cone of completely positive matrices. We then establish its strong duality to a copositive program. To exemplify the effectiveness of this equivalence result, we adopt sequential polyhedral approximation of completely-positive cones and analyze its performance numerically. We also quantify the approximation error for a quantized version of a continuous distribution and show that a semi-definite program relaxation of the equivalent problem could be a benchmark lower bound for the sender's cost for large state spaces.

The free energy principle (FEP) states that any dynamical system can be interpreted as performing Bayesian inference upon its surrounding environment. Although, in theory, the FEP applies to a wide variety of systems, there has been almost no direct exploration or demonstration of the principle in concrete systems. In this work, we examine in depth the assumptions required to derive the FEP in the simplest possible set of systems – weakly-coupled non-equilibrium linear stochastic systems. Specifically, we explore (i) how general the requirements imposed on the statistical structure of a system are and (ii) how informative the FEP is about the behaviour of such systems. We discover that two requirements of the FEP – the Markov blanket condition (i.e. a statistical boundary precluding direct coupling between internal and external states) and stringent restrictions on its solenoidal flows (i.e. tendencies driving a system out of equilibrium) – are only valid for a very narrow space of parameters. Suitable systems require an absence of asymmetries in perception-action loops that are highly unusual for living systems interacting with an environment, which are the kind of systems the FEP explicitly sets out to model. More importantly, we observe that a mathematically central step in the argument, connecting the behaviour of a system to variational inference, relies on an implicit equivalence between the dynamics of the average states of a system with the average of the dynamics of those states. This equivalence does not hold in general even for linear systems, since it requires an effective decoupling from the system's history of interactions. These observations are critical for evaluating the generality and applicability of the FEP and indicate the existence of significant problems of the theory in its current form. These issues make the FEP, as it stands, not straightforwardly applicable to the simple linear systems studied here and suggests that more development is needed before the theory could be applied to the kind of complex systems which describe living and cognitive processes.

It is a significant and challenging problem to coordinate multiple microgrids (MMGs) belonging to different entities and achieve their excellent energy-sharing performance to ensure the stability of electricity markets. This paper studies a grid-oriented energy bidding problem for MMGs with peer-to-peer (P2P) energy trading under uncertainty. A stochastic Cartel game (SCG) based strategy is developed. A stochastic Cartel nonlinear programming model is formulated to characterize the joint energy bidding, the energy production, and P2P energy transactions while minimizing the total cost for MMGs under uncertainty. A diagonal quadratic approximation method is employed to linearize quadratic terms, and the SCG problem for MMGs is further decomposed into subproblems for individual MGs based on a surrogate Lagrangian relaxation method. The equivalence of problem transformation is proved and equilibrium solutions are derived in an iterative and distributed manner. Comparisons for different strategies, models, and solution algorithms are conducted to testify the rationality and validity of the proposed strategy.

The parallel Hierarchical Dirichlet Process (pHDP) is an efficient topic model which explores the equivalence of the generation process between Hierarchical Dirichlet Process (HDP) and Gamma-Gamma-Poisson Process (G2PP), in order to achieve parallelism at the topic level. Unfortunately, pHDP loses the non-parametric feature of HDP, i.e., the number of topics in pHDP is predetermined and fixed. Furthermore, under the bootstrap structure of pHDP, the topic-indiscriminate words are of high probabilities to be assigned to different topics, resulting in poor qualities of the extracted topics. To achieve parallelism without sacrificing the non-parametric feature of HDP, in addition to improve the quality of extracted topics, we propose a parallel dynamic topic model by developing an adjustment mechanism of evolving topics and reducing the sampling probabilities of topic-indiscriminate words. Both supervised and unsupervised experiments on benchmark datasets show the competitive performance of our model.

By mass-energy equivalence, the gravitational field has a relativistic mass density proportional to its energy density. I seek to better understand this mass of the gravitational field by asking whether it plays three traditional roles of mass: the role in conservation of mass, the inertial role, and the role as source for gravitation. The difficult case of general relativity is compared to the more straightforward cases of Newtonian gravity and electromagnetism by way of gravitoelectromagnetism, an intermediate theory of gravity that resembles electromagnetism., Comment: 39 pages, 1 figure

There are exactly four surfaces of minimal degree in P 5 , up to projective equivalence. And they have the same graded Betti numbers. So it is a natural question to ask how to recognize them by their defining equations. In this paper we provide an answer to this question in terms of the rank loci of quadratic equations of those four surfaces. We show that the sets of rank 3 and rank 4 quadratic equations distinguish them.

In this study, we present a new formal method for verifying the functionality of Galois-field (GF) arithmetic circuits. Assuming that the input–output relation (i.e., the specification of a GF arithmetic circuit) can be represented as polynomials over 2, the proposed method formally checks the equivalence between GF polynomials derived from a netlist and the specification. To efficiently verify the equivalence, we employ a zero-suppressed binary decision diagram (ZDD) to represent polynomials over 2. Even though polynomial reduction is the most time-consuming process of verification (i.e., equivalence checking), our new algorithm can efficiently reduce the GF polynomials in the form of a zero-suppressed binary decision diagram derived from the target netlist. The proposed algorithm derives the polynomials representing all intermediate nodes (i.e., the outputs of all gates) in the order from primary inputs to those primary outputs that are in accordance with the reverse topological traversal order. We demonstrated the efficiency and effectiveness of the proposed method via a set of experimental verifications. In particular, we confirmed that the proposed method can verify practical GF multipliers (including those used in standardized elliptic curve cryptography) approximately 30 times faster on average and at most 170 times faster than the best conventional method.

In this paper, accelerated life test is considered when the latent failure times follow Weibull competing risks models. When both scale and shape parameters are nonconstant and affected by operating stress, inference is discussed for a constant-stress model under a generalized progressive hybrid censoring. Maximum likelihood estimates together with existence and uniqueness are established, and the approximate confidence intervals for unknown parameters are proposed based on the asymptotic theory. Further, when the distributions of failure causes have common shape or scale parameters, associated point and interval estimates are also proposed. In addition, to compare the equivalence of the parameters of different Weibull competing risks, likelihood ratio tests for interested hypotheses are presented for complementary. Finally, extensive numerical studies and a real-life example are provided for illustrations.

We show that a complex planar curve homeomorphic to the projective line has at most four singular points. If it has exactly four then it has degree five and is unique up to a projective equivalence., 35 pages

We consider the absolute stability of discrete-time Lurye systems with SISO/MIMO (non-repeated SISO) nonlinearities that are sector bounded and slope restricted. For this class of systems, we present a parametrization of Lyapunov-Lurye functional (LLF) that is the time-domain equivalence to finite impulse response (FIR) Zames-Falb multipliers. As searches over FIR Zames-Falb multipliers provide the best known results in the literature, the parametrization here provides the best-known Lyapunov function for absolute stability. A motivation of this alternative is making it easy to analyze the system in the time domain, especially when the frequency domain expression of the system is not straightforward. In this letter, we show the equivalence between the proposed LLF and FIR multipliers theoretically and numerically.

We study the problem of aggregating private information in elections with two or more alternatives for a large family of scoring rules. We introduce a feasibility condition, the linear refinement condition, that characterizes when information can be aggregated asymptotically as the electorate grows large: there must exist a utility function, linear in distributions over signals, sharing the same top alternative as the primitive utility function. Our results complement the existing work where strong assumptions are imposed on the environment, and caution against potential false positives when too much structure is imposed.

A subclass of finite Petri nets, called BPP nets (acronym of Basic Parallel Processes), was recently equipped with an efficiently decidable, truly concurrent, bisimulation-based, behavioral equivalence, called team bisimilarity. This equivalence is a very intuitive extension of classic bisimulation equivalence (over labeled transition systems) to BPP nets and it is checked in a distributed manner. This paper has three goals. First of all, we provide BPP nets with various causality-based observational semantics, notably a novel semantics, called causal-net bisimilarity. Then, we define a variant semantics, called h-team bisimilarity, coarser than team bisimilarity, for which we adapt the modal logic characterization and the axiomatization of team bisimilarity. Then, we complete the study about team bisimilarity and h-team bisimilarity, by comparing them with the causality-based semantics we have introduced: the main results are that team bisimilarity coincides with causal-net bisimilarity, while h-team bisimilarity with fully-concurrent bisimilarity.

Linear first order Riemann-Liouville fractional differential equations are studied. These new equations unify and generalize the Riemann-Liouville, modified Caputo and Caputo fractional differential equations. The equivalences between the fractional differential equations and the corresponding perturbed Abel's integral equations are obtained. These results are useful not only to study the initial or boundary value problems for nonlinear first order Riemann-Liouville fractional differential equations but also to study the solutions of the perturbed Abel's integral equations arising in a problem of mechanics and many other physical problems. The well-known Tonelli's result on solvability of the Abel's integral equation is generalized. We exhibit that there are nonconstant equilibria for some first order Caputo fractional equations. This is different from nonlinear first order ordinary differential equations which have only constant equilibria. The equivalence results are applied to generalize the classical Mean Value Theorem to the first order Riemann-Liouville fractional derivatives.

Background We aimed to verify whether the taste and chemical composition influence the selection of plants in each medicinal category, whether within a socio-ecological system or between different socio-ecological systems. To this end, we use the theoretical bases of the Utilitarian Redundancy Model and the Utilitarian Equivalence Model. We studied the local medical systems of four rural communities in northeastern Brazil, used as models to test our assumptions. Methods The data on medicinal plants and local therapeutic function were obtained from semi-structured interviews associated with the free-listing method, allowing to generate indexes of similarity of therapeutic use between the plants cited in each region. During the interviews, each informer was also asked to report the tastes of the plants cited. Subsequently, we classified each plant in each region according to the most cited taste. The data about the chemical composition of each plant were obtained from a systematic review, using Web of Knowledge and Scopus databases. Results Pairs of plants with similar tastes are 1.46 times more likely to have the same therapeutic function within a local medical system (redundancy), but not between medical systems (equivalence). We also find that chemical compounds are not primarily responsible for utilitarian redundancy and equivalence. However, there was a tendency for alkaloids to be doubly present with greater expressiveness in pairs of equivalent plants. Conclusions The results indicate that each social group can create its means of using the organoleptic characteristics as clues to select new species as medicinal. Furthermore, this study corroborates the main prediction of the Utilitarian Equivalence Model, that people in different environments choose plants with traits in common for the same functions.

In this paper, the optimal output synchronization of heterogeneous multi-agent systems is studied. To overcome the shortcoming of previous methods that require system model, a data-based optimal control policy is proposed for the output synchronization problem . Besides, the intrinsic equivalence relationship between model-based optimal solution and the proposed data-based optimal solution is proved. To solve the proposed control policy, a reinforcement learning algorithm based on measured input-output data is presented, which is different from existing model-free algorithms based on internal state. According to the algorithm, the optimal output synchronization problem of heterogeneous multi-agent systems can be solved when the full-state vector is unavailable. Finally, the effectiveness of proposed algorithm is verified by simulation examples.

We give the complete description of bijective real-linear transformations on B ( H ) , the algebra of all bounded linear operators on an infinite-dimensional complex Hilbert space H , where every unitary U ∈ B ( H ) is mapped to a unitary ϕ ( U ) . In turn, bijective real-linear maps on B ( H ) preserving equivalence by unitaries will be determined.

Vehicular communications based on IEEE,802.11p promise to improve traffic efficiency and safety in the near future. Embedded with 802.11p-compliant devices, the cooperation among connected vehicles will provide a shift in the way transportation systems operate. Nevertheless, before widespread adoption, extensive performance evaluation of the standard is in need. Due to the high cost and reasonably low availability of commercial devices, most work on VANETs is still performed using simulations. To investigate the equivalence between real experiments and simulations involving 802.11p, this article evaluates the behavior obtained by periodic beacon messages, the basis of safety applications in VANETs. Using commercial OBUs and RSUs, the results are compared with those obtained with NS-3/PhySim and Veins/MiXiM simulators. In V2I and V2V communication scenarios, three key metrics are evaluated: the maximum communication range, packet delivery rate, and packet inter-reception time. The influence of different modulations supported by 802.11p and varying vehicle speeds are also analyzed.

Recently, there has been a revival of interest in cyclic decompositions of stochastic dynamics. These decompositions consider the behavior of dynamics over the short, medium and long run, aggregating cycles of behavior into progressively larger cycles, eventually encompassing the entire state space. We show that these decompositions are equivalent to the aggregative stage of Edmonds' algorithm and that this equivalence can be used to recover well-known results in the literature.

We propose a novel formalization of roles in social networks that unifies the most commonly used definitions of role equivalence. As one consequence, we obtain a single, straightforward proof that role equivalences form lattices. Our formalization focuses on the evolution of roles from arbitrary initial conditions and thereby generalizes notions of relative and iterated roles that have been suggested previously. In addition to the unified structure result this provides a potential micro-foundation for the emergence of roles. Considering the genesis of roles may explain, and help overcome, the problem that social networks rarely exhibit interesting role equivalences of the traditional kind. Finally, we discuss extensions of the role concept to multivariate networks with actor and tie attributes by example., Social Networks, 68